using OrdinaryDiffEqLowStorageRK
using Trixi

# Up to version 0.13.0, `max_abs_speed_naive` was used as the default wave speed estimate of
# `const flux_lax_friedrichs = FluxLaxFriedrichs(), i.e., `FluxLaxFriedrichs(max_abs_speed = max_abs_speed_naive)`.
# In the `StepsizeCallback`, though, the less diffusive `max_abs_speeds` is employed which is consistent with `max_abs_speed`.
# Thus, we exchanged in PR#2458 the default wave speed used in the LLF flux to `max_abs_speed`.
# To ensure that every example still runs we specify explicitly `FluxLaxFriedrichs(max_abs_speed_naive)`.
# We remark, however, that the now default `max_abs_speed` is in general recommended due to compliance with the
# `StepsizeCallback` (CFL-Condition) and less diffusion.
dg = DGMulti(polydeg = 4, element_type = Quad(), approximation_type = Polynomial(),
             surface_integral = SurfaceIntegralWeakForm(FluxLaxFriedrichs(max_abs_speed_naive)),
             volume_integral = VolumeIntegralFluxDifferencing(flux_ranocha))

equations = CompressibleEulerEquations2D(1.4)

"""
A compressible version of the double shear layer initial condition. Adapted from
Brown and Minion (1995). See Section 3, equations (27)-(28) for the original
incompressible version.

- David L. Brown and Michael L. Minion (1995)
  Performance of Under-resolved Two-Dimensional Incompressible Flow Simulations.
  [DOI: 10.1006/jcph.1995.1205](https://doi.org/10.1006/jcph.1995.1205)
"""
function initial_condition_BM_vortex(x, t, equations::CompressibleEulerEquations2D)
    pbar = 9.0 / equations.gamma
    delta = 0.05
    epsilon = 30
    H = (x[2] < 0) ? tanh(epsilon * (x[2] + 0.25)) : tanh(epsilon * (0.25 - x[2]))
    rho = 1.0
    v1 = H
    v2 = delta * cos(2.0 * pi * x[1])
    p = pbar
    return prim2cons(SVector(rho, v1, v2, p), equations)
end
initial_condition = initial_condition_BM_vortex

cells_per_dimension = (16, 16)
mesh = DGMultiMesh(dg, cells_per_dimension,
                   coordinates_min = (-0.5, -0.5), coordinates_max = (0.5, 0.5),
                   periodicity = true)
semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, dg;
                                    boundary_conditions = boundary_condition_periodic)

tspan = (0.0, 1.0)
ode = semidiscretize(semi, tspan)

summary_callback = SummaryCallback()
alive_callback = AliveCallback(alive_interval = 10)
analysis_interval = 100
analysis_callback = AnalysisCallback(semi, interval = analysis_interval)
save_solution = SaveSolutionCallback(interval = analysis_interval,
                                     solution_variables = cons2prim)
callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback, save_solution)

###############################################################################
# run the simulation

tol = 1.0e-8
sol = solve(ode, RDPK3SpFSAL49(); abstol = tol, reltol = tol,
            ode_default_options()..., callback = callbacks);
